Customer Reviews

Algebraic Theory of Numbers: Translated from the French by Allan J. Silberger (Dover Books on Mathematics)

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Samuel's book is a classic. It is a bit "antique", certainly not the most modern introduction to algebraic number theory. The topics covered in the book are algebraic and integral extensions, Dedekind rings, ideal classes and Dirichlet's unit theorem, the splitting of primes in an extension field and some Galois theory for number fields. So the range of topics is quite small (and the book is short, ~100 pages).

And yet I love this book. It is crystal clear, well written and well structured; it is quite dense (especially the last chapter) and makes the beginning student of algebraic number theory think a lot, but without ever getting too heavy to digest. The list of problems is fantastic: there are many very concrete problems which sharpen your understanding of the material considerably. And last but not least, it is ridiculously cheap.

I recommend this to anyone who wants to learn the basic material about number fields. Without any hesitation.

(I have read this book in French, so can't comment on the translation). This is the best introduction to number theory, and the Dover price certainly can't be beat. The one problem with this book is that the perspective is very Bourbakist, and so the arguments do not tend to be constructive, so you might want your next book to be A Course in Computational Algebraic Number Theory (Graduate Texts in Mathematics)

It's a little dense, and some proofs are lacking detail, but otherwise a great book. Extensive subject covered in one semester's worth of reading.

This is a lovely, lovely book -- the first I ever read on algebraic number theory. It is spare and direct, and a great introduction to the field.

Never got shipping confirmation email but customer service was very quick to respond to my question about the shipping status.